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A061922 Xcatalans - produced as a self-convolved sequence like Catalan numbers (A000108) but use carryless GF(2)[ X ] polynomial multiplication. 6

%I

%S 1,1,2,5,14,42,132,421,1382,4478,15580,54114,181676,650484,2289320,

%T 8028901,28045302,103229014,372640460,1336511110,4882492452,

%U 17534836812,63692926552,234287550818,868236370364,3281589811404

%N Xcatalans - produced as a self-convolved sequence like Catalan numbers (A000108) but use carryless GF(2)[ X ] polynomial multiplication.

%C Shifts one place left when Xmult-convolved (XMULTCONV) with itself.

%p Xcatalans(30); Xcatalans := proc(upto_n) local a,i,k; a := [1]; for i from 1 to upto_n do a := [ op(a), add(Xmult(a[k],a[i-k+1]), k=1..i)]; od; RETURN(a); end;

%p XMULTCONV := proc(a,b) local c,i,k,n; n := min( nops(a), nops(b) ); c := []; for i from 0 to n-1 do c := [ op(c), add(Xmult(a[k+1],b[i-k+1]), k=0..i)]; od; RETURN(c); end;

%Y For Xmult, see A048720 (Xmult table) or A048631 (Xfactorials). Other self-convolved sequences: A000108, A007460 - A007464, A025192.

%K nonn,easy,eigen

%O 0,3

%A _Antti Karttunen_, May 15 2001

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Last modified December 5 21:00 EST 2019. Contains 329779 sequences. (Running on oeis4.)